Completion Necessity for Readout-Non-Equivalent Domains
Certified active slot failure and the obstruction to full public closure
Authority role
Establishes the obstruction criterion: readout loss becomes a genuine public obstruction only when it is certified as an active, uncleared failure of an essential public closure slot.
Summary
Proves the precise additional condition under which a lost realization role becomes a genuine obstruction: a certified active failure profile on an essential closure slot with no checked repair or public surrogate. Blocks the common overread that readout loss automatically obstructs anything, instantiates the theorem for first-order proof targets, and emits a completion-need record for downstream categorical completion theory.
Notes
Reading notes
Paper 1 is a non-equivalence principle, not an obstruction machine. This paper supplies the missing certificate: it fixes a public target, a frozen readout state, and a lost realization role, and defines essential closure slots generated from the target specification alone.
Definition — Certified active failure profile
A certified verdict that a lost role is required by an essential slot and that no checked repair, discharge, or public surrogate clears that slot.
Theorem — Bridge principle (informal)
Readout loss plus certified active slot failure blocks sound full public closure. Neither alone suffices.
The first-order instantiation distinguishes a checker-accepted derivation from resolved public proof closure from the frozen base, and is explicitly conditional on declared certified subcalculi.
Cite this paper
Rodgers, Jeremy. (2026). Completion Necessity for Readout-Non-Equivalent Domains (v5). https://doi.org/10.5281/zenodo.21184388